Financial Engineering Research at McCormick

Financial Risk Management

Market risk is a risk of adverse changes in prices or rates, such as interest rates, foreign exchange rates, stock prices, and commodity and energy prices. Credit risk is a risk of default on a financial obligation, such as a bond, loan, or lease. Aspects of financial risk management include measuring the risk of a financial transaction (transaction risk) or of a large investment portfolio (portfolio risk), an entire financial institution (enterprise risk), or a network of financial institutions (systemic risk), exploring ways to reduce risk, and determining an adequate capital reserve against potential losses. Risk management requires good models of extreme financial events and the capacity to compute the risk of a large portfolio in a timely manner.

Prof. Linetsky is working on mathematical modeling of credit risk in several settings. His research covers corporate bonds, credit derivatives, and default correlations among multiple borrowers, including the phenomenon of default contagion. He is also working on asset financing, such as home mortgages and loans or leases backed by aircraft and other heavy equipment.

Prof. Staum is studying systemic risk in networks of financial institutions. This work is aimed at helping international financial authorities design new regulations to increase the stability of the global financial system. An analysis of the network of obligations among banks and their counterparties reveals the threats to the whole financial system and helps in designing strategies to mitigate them.

Profs. Nelson and Staum are working on computationally efficient Monte Carlo simulation algorithms computer simulation algorithms for measuring the risk of a portfolio or evaluating the effectiveness of strategies for hedging risk. Often, risk management simulations must be completed within just a few hours; within that time frame, these algorithms provide answers that are dozens of times more precise than those of earlier methods. Their research group has also created an algorithm that harnesses the parallel computing power of inexpensive graphics processing units to make risk management simulations timely for even the largest firms' portfolios.

Prof. Nocedal is studying the formulation and solution of convex optimization problems arising in the minimization of conditional value at risk.

 

Portfolio Optimization

The problem of portfolio optimization is to find an investment strategy that best fits a decision-maker's needs and preferences. Portfolio optimization problems occur throughout the financial services industry as pension funds, mutual funds, insurance companies, university and foundation endowments, and individual investors face the fundamental problem of allocating their capital among different investments in order to generate investment returns sufficient to achieve a particular goal, such as meeting future pension liabilities. Portfolio optimization can be quite computationally challenging. It is a high-dimensional problem when there are many securities to invest in and many times at which the portfolio can be updated. Taxes and restrictions on the investment strategy may introduce features such as nonlinearity and integer constraints.

Prof. Kao has studied the computational complexity of portfolio optimization algorithms involving large numbers of securities.

Prof. Mehrotra has developed stochastic nonlinear (semidefinite and convex) models and algorithms for asset-liability management problems.

Prof. Nocedal has studied the solution of nonlinear portfolio optimization problems. The KNITRO software package developed jointly by Ziena Optimization Inc and Northwestern University is used by some of the largest financial institutions to solve portfolio problems involving thousands of securities.

 

Derivative Securities

Derivative securities, such as stock options and commodities futures, have payoffs that are related to the value of an underlying asset, such as a stock or commodity. Derivative securities facilitate the transfer of financial risk from hedgers, who wish to reduce their risk exposure, to investors, who are willing to take risk when it comes with a sufficient possibility of gain. For example, a company may be exposed to the risk of increasing commodity and energy prices that will make future production more expensive or to the risk of increasing interest rates that will make future financing more expensive. The company can hedge those risks by entering into financial contracts that act as insurance, protecting it against adverse market events. Important segments of global derivatives markets include interest rate derivatives, currency derivatives, equity derivatives, commodity and energy derivatives, and credit derivatives.
The classic problem of financial engineering is to find the relationship between the derivative security's price and that of the underlying asset. Research topics include the development of realistic stochastic models for underlying assets and market variables, leading to more accurate prices for derivative securities, and the development of efficient algorithms to compute derivatives prices quickly.

Prof. Linetsky has worked on many aspects of derivative securities modeling and valuation. He has developed stochastic models for equity, foreign exchange, interest rate, and credit derivatives. He has also devised analytical and computational methods for derivative security pricing, based on spectral expansions, integral transforms, and numerical solution of partial differential equations. He currently works on modeling and valuation of commodity and energy derivatives.

Prof. Nocedal has developed an efficient computational algorithm to solve linear complementarity problems arising in the valuation of American-style options.

Prof. Olmstead has done consulting on stock options trading strategies and recently published a book "Options for the Beginner and Beyond."

Prof. Staum has studied the valuation of derivative securities in incomplete markets. Incomplete markets are those in which perfect risk transfer is not possible, so that a derivative securities trader is left bearing some risk. He has worked on the method of good deal bounds, which allows a trader or investor to determine the prices at which he or she is willing to buy and sell a derivative security and bear the resulting risk.